Teacher noticing--i.e., attending to and interpreting--students' mathematical thinking is a predominant framework in preparation programs for pre-service mathematics teachers, based on the assumption that they should learn to notice early in their training to acquire the expertise needed in their professional lives. Most research on this topic…

Research on teachers' noticing of student mathematical thinking has typically focused on how a teacher attends to, interprets, and determines a response to an individual student contribution in isolation from the broader mathematical classroom context. This research focus is not nuanced enough, however, to fully account for the complex noticing…

In this theoretical article, we propose a conceptualisation of noticing, drawing on our enactivist perspective, which takes account of what is now known about human cognition, and from which we draw out implications for how noticing develops. We review past work on mathematics teacher noticing and note the dominance of a paradigm of taking…

Mathematics standards and practices highlight the vital role that language plays in mathematics education. However, there remains a common misconception that mathematics is somehow language-free or less linguistically demanding than other content areas. This qualitative study describes an intervention implemented in six elementary mathematics…

In this study, we examine "what went wrong" in our professional development program for encouraging cognitively demanding instruction, focusing on the difficulties we encountered in using an observational tool for evaluating this type of instruction and reaching inter-rater reliability. We do so through the lens of a discursive theory of…

This study explores secondary-school mathematics teachers' noticing of Critical Events Associated with Argumentation (CEAs), moments when students' reasoning or interactions become evident, offering teachers opportunities to promote argumentation in the classroom. Thirty-one teachers analyzed a written classroom scenario, identifying CEAs,…

We contribute to the understanding of teacher noticing by focusing on what a teacher may notice in students' mathematical contributions in the context of problem-based lessons. Complementing approaches to research on noticing that focus on individual teachers' perceptual, cognitive, or situated skills, this conceptual article offers four…

Background and Aims: Students with intellectual disability benefit from high-quality instruction in reading and mathematics. Methods: This Theoretical Paper outlines the need for effective, evidence-based instructional practices for this population and the potential for observation research to inform such advancements. We report our systematic…

This study explores variations in prospective teachers' (PTs') noticing of students' mathematical thinking based on narrative writing within the context of a practicum course. The research involved eight PTs, each of whom produced ten weekly narratives throughout the course duration. Most PTs displayed noticing abilities within the average range,…

In this article, the authors share two examples of student engagement in visible, mathematical thinking through a Chalk Talk within the four walls of the classroom, as well as the connected spaces of online learning. Five steps for facilitating the Chalk Talk are outlined, with descriptions of teacher moves for each step. The silent thinking…

The study investigated the impact of pedagogies of practice approach on pre-service teachers' professional noticing skills in perimeter and area measurement concepts. Thirty-two pre-service teachers engaged in a video-based module situated in pedagogies of practice framework, and the analysis of three pre-service teachers was provided for in-depth…

Considerable research has been conducted on the critical role of gesture and action in children's mathematical thinking. However, teacher professional development (PD) has not tended to include specific supports for attending to nonverbal student thinking. In this Brief Report, we argue for including supports for multimodal teacher noticing in…

Background and Aims: Students with intellectual disability benefit from high-quality instruction in reading and mathematics. Methods: This Theoretical Paper outlines the need for effective, evidence-based instructional practices for this population and the potential for observation research to inform such advancements. We report our systematic…

Background: Numerous studies show that active and engaging classrooms help students learn and persist in college, but adoption of new teaching practices has been slow. Professional development programs encourage instructors to implement new teaching methods and change the status quo in STEM undergraduate teaching, and structured observations of…

Most studies of mathematics teacher noticing employ information-processing-based models of noticing. While information processing has been used productively to research the cognitive requirements of noticing, critics have argued that these accounts conceptualise noticing as a relatively passive and mental act. This paper demonstrates how an…